Molecular orbital theory, bond energy and dipole moment

Chemistry · Chemical bonding. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

In molecular orbital theory, atomic orbitals of two atoms combine to form molecular orbitals that belong to the whole molecule. Two atomic orbitals give two molecular orbitals: a bonding orbital of lower energy and an antibonding orbital (marked *) of higher energy. Electrons fill them from the lowest energy upwards, following the Pauli principle and Hund's rule.

The bond order tells how many bonds join the two atoms. A bond order of zero means the molecule does not form. Unpaired electrons make a substance paramagnetic (attracted by a magnet).

Bond energy and bond length measure the strength and size of a bond. The dipole moment measures how polar a molecule is. It depends on shape as well as on bond polarity.

Rules to remember

bond order = (number of bonding electrons − number of antibonding electrons) ÷ 2.
H₂: (2 − 0) ÷ 2 = 1. He₂: (2 − 2) ÷ 2 = 0, so it does not exist. N₂: (10 − 4) ÷ 2 = 3. O₂: (10 − 6) ÷ 2 = 2.
O₂ has two unpaired electrons, one in each of the two π*2p orbitals, so oxygen is paramagnetic.
A higher bond order means a shorter and stronger bond.
Bond energy: the average energy needed to break one mole of a given bond in the gaseous state, in kJ mol⁻¹. It is larger for shorter, multiple and more polar bonds: H−F > H−Cl > H−Br > H−I; C≡C > C=C > C−C.
dipole moment = charge × distance between the charges (μ = q × r). Unit: debye, D. 1 D = 3.336 × 10⁻³⁰ C m.
Symmetrical molecules have zero dipole moment because the bond dipoles cancel: CO₂ (linear), BF₃ (trigonal planar), CH₄ and CCl₄ (tetrahedral). H₂O (1.85 D, bent) and NH₃ (about 1.5 D, pyramidal) are polar.

Common mistake

Students think polar bonds always make a polar molecule. In a symmetrical molecule such as CO₂ or CCl₄ the bond dipoles cancel, so the dipole moment is zero.

Worked example

N₂ has 10 bonding and 4 antibonding electrons. An electron is removed from a bonding orbital to form N₂⁺. What is the bond order of N₂⁺, and is its bond stronger or weaker than that of N₂?

N₂⁺ has 10 − 1 = 9 bonding electrons and still 4 antibonding electrons.
Bond order = (9 − 4) ÷ 2 = 2.5.
The bond order of N₂ is (10 − 4) ÷ 2 = 3, which is higher.

Answer: Bond order 2.5; the bond in N₂⁺ is weaker and longer than in N₂.

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Chapter 6: Chemical Bonding

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